The short version of this very long post1 is that the Commission’s current policy of applying the concept of recidivism to the highest level parent that exercises decisive influence over the infringing company appears to unduly punish undertakings that sell a large number of different products as compared to undertakings that sell only a small number. The likelihood of being a recidivist is massively influenced by the product range of the company and not by the propensity of the company to cartelise.

For the sake of simplicity the rest of this post assumes the existence of a multi-product firm with each product being sold in a different subsidiary.

The increase in fine for recidivism under the Commission’s 2006 Fines Notice appears to be imposed more because of the extent of the product range of the undertaking than because of the undertaking’s relative culpability (it’s propensity to participate in a cartel). Obviously, all other things being equal, an undertaking with several subsidiaries2 is more likely to be a recidivist than an undertaking with a single subsidiary; that would not make a recidivism uplift for the multi-product undertaking unfair. But the increased probability of being a recidivist does not increase linearly with an increase in the number of subsidiaries – it increases far more quickly. You might think that an undertaking with ten subsidiaries is ten times more likely to be a recidivist than an undertaking with a single subsidiary. In fact it is fifty times more likely.

It is this lack of linearity that makes the Commission’s current approach to recidivism dubious. The recidivism uplift is going to be applied to companies with more subsidiaries, rather than companies with greater culpability.

What follows tries to explain this using basic probability. Be warned; it is quite long.

For those happier with probabilities and tables, then attached you will find a spreadsheet – Recidivism-probabilities – where you can alter the basic assumptions and see what impact that has on the probabilities.

Here is a static table, setting out the assumptions and probabilities on which the text below is based.

Probability Equivalent to once every…
Probability of infringement per year 0.0100 100 years
Reduction in probability after first infringement 50% 0.0050 200 years
Reduction in probability after third infringement 50% 0.0025 400 years
Number of subsidiaries (assuming for simplicity one sub=one product)
1 10 383 50 100
Probability of undertaking infringing the competition rules sometime in a ten year period 9.6% 63.4% 97.8% 99.3% 99.996%
Probability of the same undertaking also infringing the competition rules in a second ten year period 0.5% 25.0% 83.2% 91.2% 99.3%
Probability of the same undertaking also infringing the competition rules in a third ten year period 0.0% 5.5% 51.1% 65.1% 91.2%



Many competition authorities punish repeat offenders more severely, but authorities are not consistent in what constitutes a repeat offence in terms of:
– whether a repeat offence should be measured by the product, the company, or the corporate group (the “recidivism entity”); and
– the time between the definitive finding of one infringement and the beginning of the next (the “recidivism time period”).

This post looks only at the first of these, the recidivism entity, and for the sake of brevity does not look into the recidivism time period. There are also many other aspects of recidivism policy not covered in this post – whether a cartel followed by a vertical distribution infringement should be regarded as recidivism, whether a national distribution infringement followed by a global abuse should be regarded as recidivism, whether a comparatively small cartel justifies a recidivism uplift in a comparatively large and later cartel, and so on.

Of course, punishing repeat offenders more severely is generally accepted as a good idea and is far from unique to competition enforcement. If someone breaks a law, the penalty is often supposed to both punish the offender for the particular offence, and deter the offender from committing any future offence (and deter others more generally but that’s not relevant here). So if the same offender reoffends, it is reasonable to assume that the punishment for the first offence was not sufficiently deterrent, and the punishment for the second offence should be increased.

When looking at an individual – say a bank robber – the principle is relatively straightforward. An individual who robs a bank, is then caught and punished, and then robs another bank, is a recidivist.

When applied to corporate law-breaking, it is a little more complicated. When looking at whether an offence is a repeat offence, do you look at whether the conduct was carried out by the same employee, the same division, the same legal entity, or the same undertaking? Which recidivism entity you take into account makes a big difference.

The European Commission’s policy on recidivism is not restricted to the legal entity which was involved in a cartel, but extends to the ultimate parent which exercises decisive influence over that entity, and 100% ownership leads to a presumption of decisive influence which is in practice difficult if not impossible to rebut.

A Simplified Example

So how does that policy affect (1) a single product firm as compared to (2) a corporate group with a parent and, say, 100 subsidiaries? The approach I have taken here is to assume all other characteristics of the firms are the same – so eliminating all variables other than the number of the subsidiaries. I assume that the risk of each subsidiary entering into a cartel is the same, the propensity of all of the industries to cartelise is the same, and so on. Then I look at the probability of recidivism for companies with different numbers of subsidiaries.

The Problem with Probability

One of the problems with probability is that for many people, and certainly for me, it is deeply counter-intuitive. If a roulette wheel comes up black three times in a row, I want to bet on red. But if the wheel is true, then the probability of a red after three blacks is the same as the probability of a black after three blacks. So if a roulette wheel comes up black ten times in a row, there’s a temptation to think that the wheel is rigged. But given the number of casinos and roulette wheels in the world, and spins of those roulette wheels every day, I would guess – and I haven’t even tried to work this out – that a roulette wheel hitting black ten times in a row happens every few days. (This is the same idea as an individual winning a lottery twice; it’s very unlikely to happen to any one individual, but given the number of lotteries and players in the world, it’s also very likely to happen to someone.) Thinking otherwise is often called the gambler’s fallacy. This is how casinos make their money, and is one of the reasons I don’t gamble.

The counter-intuitive nature of probability is one of the reasons that in the rest of this post, I try and express the probabilities in different ways: some readers may find one type of example easier to grasp than another. I express the probabilities as a fraction of 1 (1 being certainty), as a percentage, and as a relationship between a large number of – hypothetical – companies and the subset of those companies that would, probabilistically, engage in cartels. For those readers with a better grasp of probability theory than I, this will likely be annoyingly repetitive. My apologies.

A Single Product Company

Take a single-product company’s likelihood of entering into a cartel. There are many factors that might influence this – the type of industry, the health of the economy as a whole, the health of that particular industry, the corporate culture, the company’s emphasis on competition compliance, and so on. All of these could be combined to come up with a measure of how likely that company is to engage in a cartel in any given year.

A hypothetical probability of it entering into a cartel

In the real world there is no way to look at any company and come up with an even vaguely reliable estimate of such a measure. But for the purposes of this post, the precise number does not really matter. All that matters is that we imagine a hypothetical single product company, attribute to it a probability, and attribute that same probability to each product-selling subsidiary of the 100 product undertaking. That gives you an indication of how, controlling for all other factors, the likelihood of companies entering into cartels is related to the number of products that that company sells. In particular this controls for their propensity to cartelise.

The first cartel

So, for example, a company that manufactures widgets might, taking into account all of the factors above, have a probability of 0.01 of engaging in a cartel in a given year. In the same way that rolling a dice gives a 1 in 6 (roughly 0.17) chance of rolling a 6, a probability of 0.01 is a 1 in 100 chance. After six rolls of the dice, you are very likely to have rolled a six; after one hundred years, our widget company is very likely to have engaged in at least one cartel.

Now 1 in 100 years seems a pretty low probability of entering into a cartel (from the perspective of a competition authority, if a company only engaged in one cartel every one hundred years, then they’re probably quite law-abiding). It seems a low estimate for many companies, particularly as very few companies last for a hundred years. But I’m trying to use numbers that are the least favourable to the conclusion that I draw at the end. I should note though that is one of the assumptions in this post I am most concerned about. Some companies seem to have sufficiently good compliance that they simply do not enter into cartels. If the starting assumption is that perfect compliance is possible, then the conclusions of this post may well be completely wrong.

If our single-product company has a probability of 0.01 of entering into a cartel in any given year, then over ten years, the probability of it entering into at least one cartel is about 0.096 or 9.6%. Roughly a 1 in 10 chance. So far, so, perhaps, obvious.

Put another way, if we take 10 000 single-product companies with the same characteristics, then roughly one in ten of them – around 960 – will enter into at least one cartel in any ten year period. The reason for using such a large number of companies as a point of comparison will, I hope, become clear.

The second cartel

Let’s assume that our company is one of the 960. It enters into a cartel sometime in that ten year period, and is caught and punished. As a result, it works hard at educating its employees about the competition rules, and successfully halves its chances of entering into a cartel in the future. So from a 0.01 probability of entering into a cartel – once in a hundred years – it then has a 0.005 probability – once in two hundred years. All of the other 959 companies do the same.

Bear with me.

What are the chances that our company – or any of the other 959 companies – having entered into a cartel in that first ten year period, and then having improved its compliance, nevertheless also enters into at least one cartel in a second ten year period? About 0.0047, or 0.47%. That’s a pretty low percentage; at about 200/1 against, not something anyone would likely bet on.

We started with 10 000 companies. Of these, 960 would enter into that first cartel in the first ten year period, and 47 of those 960 would enter into a second cartel in that second ten year period.

Round three.

The third cartel

Let’s assume that our cartel-prone company – and the 46 others – is caught, again, and punished for this second cartel. And they redouble their compliance efforts. So from a 0.005 probability of entering into a cartel in any given year, any one company now has a 0.0025 probability. One in four hundred years.

So given this further improvement in compliance, what are the chances of our widget company messing it up once again, and entering into at least one more cartel in a third ten year period? About 0.0001 or 0.001%. Or, of the original 10 000 companies, of which 960 entered into a first cartel, of which 47 entered into a second cartel, only 1 entered into the third.

Probability of cartelizing Equivalent to…
First Cartel 9.56% 960 companies out of 10 000
Second Cartel 0.47% 47 companies out of 10 000
Third Cartel 0.0116% 1 company out of 10 000

That looks good. Our single product company – and its 9 999 equivalent companies – has the incentive to keep improving its compliance, and keep reducing the chances of it engaging in cartels. On the above numbers, only 1 in 10 000 will enter into three cartels.

So much for a single-product company. Most companies produce more than just a single product. As we will see, the more products are produced (assuming for simplicity that each product is produced in a separate subsidiary), the greater the likelihood of a company being a recidivist. But the increase is far from linear.

A 100 Product Company

From a single-product company that just produces widgets, let us take an undertaking that produces one hundred different products, each in a different subsidiary.

The same hypothetical probability

Let us assume that the likelihood of each subsidiary entering into a cartel is the same as the widget company described above – 0.01. Let us also assume that if a subsidiary is caught in a cartel, then not only does that subsidiary increase its compliance efforts, but so does the entire group – which is exactly what a competition authority would want to happen.

Let us also assume that whether one subsidiary does not make it any more or less likely that another subsidiary will also enter a cartel (in terms of probability, that they are independent events), save for the undertaking-wide increase in compliance efforts after the fact.

The first cartel

In a ten year period, what are the chances of this 100-subsidiary company entering into at least one cartel in at least one of its subsidiaries? It is probably no surprise that it’s almost certain – over 99.99% (as opposed to about 9.6% for the single-product widget company). So if we imagine 10 000 one hundred product companies, just as we imagined 10 000 single product companies, then in a ten year period, 9 999 of those one hundred product companies will enter into a cartel (as opposed to about 960 single product companies).

Not so good for the 100-subsidiary company.

Note that the probabilities here are roughly linear – a 100-subsidiary company has roughly 100 times the probability of entering into at least one cartel than a one subsidiary company. The linearity breaks down, however, as soon as we look at recidivism.

Let us assume that the 100-subsidiary company puts in place the same additional compliance efforts as the single-subsidiary company, and does so across all 100 subsidiaries. It works just as hard at educating its employees about the competition rules (harder even, given that it has to roll out this compliance in 100 subsidiaries), and successfully halves any subsidiary’s chances of entering into a cartel in the future. So from a 0.01 probability of entering into a cartel – once in a hundred years – each subsidiary has a 0.005 probability – once in two hundred years. (Just as the single subsidiary company above.)

So what are the chances of a 100-subsidiary company entering into at least one cartel in the second ten year period?

The second cartel

We obviously expect to see the likelihood of it engaging in a second cartel after the first to be much less likely. For our single-subsidiary company above, the probability of it engaging in the first cartel was 9.6%, and a second cartel after the first was only 0.47%. But for a 100 subsidiary undertaking we only get a decrease from 99.99% to 99.33%. For every 10 000 undertakings, 9999 would enter into a first cartel, and 9933 would enter into a second. Not great. And bear in mind that this 100 subsidiary undertaking’s compliance efforts in every one of its subsidiaries are equal to that of the single product company.

The third cartel

OK, but what if our 100 subsidiary company redoubles its compliance efforts once again, just like the widget company? What are the chances that it will enter a third cartel in a third ten year period? 91.2%.

If we were faced with 10 000 undertakings, each of which had 100 subsidiaries, then 9999 would enter into a first cartel, 9933 would enter into a second, and 9120 would enter into a third.4

Comparing the single product widget company and the 100-subsidiary multinational:

Probability of cartelizing Equivalent to…
First Cartel 9.56% 99.99%
Second Cartel 0.47% 99.33%
Third Cartel 0.0116% 91.2%
Tentative Conclusions

If the law should try to treat like cases alike and different cases differently, then it’s worth asking how compliant would the 100 subsidiary company have to be at the start, to put their probability of entering the third cartel down to the level of the single product company? Roughly 0.00022, or a cartel every five thousand years. Or, if we assume that a company with that kind of compliance record can’t improve it further, and its compliance therefore cannot not improve after each infringement, then 0.00011, or a cartel every ten thousand years. That is a rather tough objective.

You can look at the same numbers from a different perspective. If we again keep the probability of entering into a cartel at 0.01 as for the single product widget company, how many subsidiaries would a company need for it to become more likely than not (a probability of more than 50%) that a multi-subsidiary company will enter into three cartels on the terms described above? About 38.

You can change the assumptions, and I encourage you to do so. You can download the spreadsheet and change the probabilities for the first, second and third cartels, and change the number of subsidiaries, and see what difference that makes.

There may of course be good reasons why larger undertakings should be held to a higher standard and exposed to a greater risk of a fines increase for recidivism: larger corporations can better afford compliance programmes, training and monitoring, for example. But the way the Commission’s recidivism policy operates doesn’t put a slightly higher standard on multi-product companies, it puts an much higher standard on them, possibly an impossibly higher standard.

But going to the opposite extreme, it is fairly clear that a recidivism policy based solely on the product itself would be too narrow. If a CEO was personally implicated in three cartels, then the fact that the cartels were in three different subsidiaries of his/her 100-subsidiary undertaking should not be enough to escape a recidivism uplift for the group as a whole.

A properly drafted recidivism policy that truly identified recidivists, and properly reflected propensity to enter into cartels would have to look at a range of factors. But ignoring the number of products sold by a company means that the current Commission policy when assessing recidivism seems to punish inappropriately multi-product undertakings.